deffunc H₁( set , Function of (Inf_seq S),BOOLEAN) -> Element of BOOLEAN = Next_univ ($1,$2);
for g1, g2 being set st g1 in ModelSP (Inf_seq S) & ( for t being set st t in Inf_seq S holds
( H₁(t, Fid (f,(Inf_seq S))) = TRUE iff (Fid (g1,(Inf_seq S))) . t = TRUE ) ) & g2 in ModelSP (Inf_seq S) & ( for t being set st t in Inf_seq S holds
( H₁(t, Fid (f,(Inf_seq S))) = TRUE iff (Fid (g2,(Inf_seq S))) . t = TRUE ) ) holds
g1 = g2 from MODELC_1:sch 3();
hence for b₁, b₂ being Element of ModelSP (Inf_seq S) st ( for t being set st t in Inf_seq S holds
( Next_univ (t,(Fid (f,(Inf_seq S)))) = TRUE iff (Fid (b₁,(Inf_seq S))) . t = TRUE ) ) & ( for t being set st t in Inf_seq S holds
( Next_univ (t,(Fid (f,(Inf_seq S)))) = TRUE iff (Fid (b₂,(Inf_seq S))) . t = TRUE ) ) holds
b₁ = b₂ ; :: thesis: verum